In this thesis reflectivity seismic inversion is applied using basis pursuit technique which reconstruct subsurface by yielding reflectivity series in high resolution from post-stack seismic data. The formula of basis pursuit optimization and the incorporation of prior assumption and information will be explained briefly further in the thesis.

Basis Pursuit Inversion is one of many inversion methods in time domain utilizing L1 constraint least square problem. Similar to Sparse Spike inversion (SSI) but different in the way of yielding solution. In BPI the primal dual solution will be used while SSI is using the simplex algorithm and threshold system in yielding reflectivity. BPI is done by creating a dictionary matrix containing reflectivity function, where the summation of these reflectivity function will be multiplied by certain coefficient producing seismic trace in representation of superposition.

In the dictionary matrix, BPI incorporating wedge model constructed from the dipole decomposition theory which decompose thin bed reflector pair into odd and even pairs. Later, in the synthetic study, sensitivity case towards inaccurate wavelets and noises will be presented, showing that BPI has the ability to yield relatively stabil results, also comparison of reflectivity gained from BPI and SSI will be shown.